Numerical modeling of pressure-reducing valves in

Numerical modeling of pressure-reducing valves in water distribution network systems -. U. S. PANU Can. J. Civ. Eng. Downloaded from www.nrcresearchpress.com by Nanjing University of Posts and Telecommunications on 06/04/13 For personal use only.

Department of Civil Engineering, Lakehead University, Thunder Bay, Ont., Canada P7B 5E1 Received May 19, 1989 Revised manuscript accepted January 26, 1990 Computer models are no longer viewed as exotic luxuries, rather they are being increasingly accepted as necessities for effective planning and operation of water distribution systems. In large networks, pressure-reducing valves (PRVs) are common water appurtenances. However, through the use of the Hazen-Williams friction factor, there are difficulties in representing PRVs in network-analysis models. This paper focuses on these difficulties and suggests a procedure for resolving them through the use of modified Hazen-Williams friction factor. The effectiveness of the proposed modification in representing PRVs in the WATER model is demonstrated. Key words: network analysis, numerical modeling, hydraulics, municipal, water distribution, PRV representation, friction coefficient, Hazen -Williams, flow rate, simulations. Les modkles B ordinateur ne sont plus vus comme des luxes exotiques; au contraire, ils sont de plus en plus acceptks comme des nCcessitCs pour la planification et l'opkration efficaces des systkmes de distribution d'eau. Dans les grands rCseaux de tuyauteries d'eau, les soupapes B riduction de la pression (((pressure-reducingvalves*, ou PRVs) sont frCquemment prksentes. Pourtant, il y a des difficult& B reprksenter les PRVs avec I'usage du facteur B frottement de Hazen-Williams. Cet article concentre sur ces obstacles et suggkre une mCthode pour les Climiner en utilisant un facteur modifit! de Hazen-Williams. L'efficacitC de la modification proposCe en reprksentant les PRVs dan le modkle WATER est dCmontrCe. Mots clds : analyse de rCseaux, modkles numkriques, hydrauliques, distribution d'eau, reprksentation des PRVs, coefficient de frottement, Hazen-Williams, Ccoulement, simulations. Can. I. Civ. Eng. 17, 547-557 (1990)

Introduction Water distribution networks are increasingly planned, designed, and operated with the aid of network-analysis models (Gupta et al. 1980). Currently available models are capable of determining flows and energy losses in various water appurtenances such as pressure-reducing valves, check valves, booster pumps, pressure-sustaining valves, and other appurtenances. Though the pressure-reducing valves (PRVs) are common appurtenances in large networks, an evaluation of their performance using the network-analysis models is difficult. This difficulty arises owing to the manner in which the HazenWilliams pipe friction factor is used in representing the PRVs in these models. With one such model, namely the WATER model (Municipal Hydraulics 1982), it was observed that PRVs performed effectively within their operating range; however, their performance became unacceptable once they reached the full-wide-open condition. For example, whenever this condition was reached in the WATER model, an increased flow rate through the PRVs was produced by the model to maintain a constant downstream pressure. Currently, the problem arising because of inadequate representation of PRVs in network-analysis models and especially in the WATER model is handled by a trial-and-error procedure. As a result, the use of these models becomes inefficient and time consuming. This paper addresses issues related to PRVs representation in network-analysis models through the use of a modified Hazen Williams friction factor. The effectiveness of the suggested procedure is shown in the WATER model. NOTE:Written discussion of this paper is welcomed and will be received by the Editor until December 31, 1990 (address inside front cover).

Printed in Canada 1 Imprim6 au Canada

model: a brief description The WATER model used in this paper is the personalcomputer version of the mainframe computer model developed by Municipal Hydraulics (1982) to simulate the water distribution system of a city or municipality. This model, in addition to a network of pipes, can simulate pumps at source (i.e., reservoir), booster pumps, pressure-reducing valves, and check valves. The latest version of this model capable of handling a network of 750 pipes and 750 pipe junctions or nodes is used in this paper. The WATER model is based on the Hazen-Williams equation for relating the pipe flow to energy loss. The model simulates a water distribution network (i.e., the specified flows or pressures at nodal points) based on steady-state flow condition and by employing a computer algorithm (Epp and Fowler 1970) based on the Newton-Raphson method of solving a set of simultaneous nonlinear equations of the system. Because the use of the Newton-Raphson method in water networks was first made by Hardy Cross (1936) for solving one nonlinear equation with one unknown, independent of other nonlinear equations of the system, it is commonly referred to as the Hardy Cross method. The WATER model is user-friendly, especially when used with the WATmdata input package for preparing input-data files. Because ~ A T E Ris a propriety model, additional technical information is only available from Municipal Hydraulics (1982). WATER

Considerations concerning PRV representation A PRV is a mechanical device used in water distribution networks to maintain water pressure below a safe pressure limit in pipes. At desired locations in such Systems, the PRVs are installed to connect low-pressure pipe lines to high-pressure

Can. J. Civ. Eng. Downloaded from www.nrcresearchpress.com by Nanjing University of Posts and Telecommunications on 06/04/13 For personal use only.

548

CAN. J. CIV. ENG. VOL. 17, 1990

pipe lines. In such systems, for example, whenever the pressure in a low-pressure line drops below a desired value, the PRV begins to open to allow water flow from the highpressure line to the low-pressure line. As a result, the flow rate through the actual PRV increases up to the maximum allowable flow rate when the PRV reaches full-wide-open condition. However, irrespective of water pressures in either the high or the low water pressure pipe line, the flow rate through the actual PRV cannot exceed its maximum allowable flow rate. It is in this context that the network-analysis models and in particular the WATER model have been found to produce excessive flow rates through the "numerical" PRV. Concerns related to unsatisfactory performance of network-analysis models form the basis of corrective measures and modifications presented below. Energy loss across a water appurtenance Before presenting the modifications and their use in WATER model, it is useful to examine some of the basic equations governing water flow through pipes. These equations are utilized later in the development of a modified Hazen -Williams friction factor for representing PRVs. The energy loss in a pipe, bend, valve, and other appurtenances is commonly referred to as the local head loss and can be expressed as

where g is the acceleration due to gravity; and hpipe,k, A, and Q are, respectively, the local head loss, the local head-loss coefficient, the cross-sectional area, and the flow rate in a pipe. For various water appurtenances, the values of k are experimentally determined based on turbulent flow (Simon 1981) and have been found to be independent of the effect of Reynold's number (Boyle 1986). The term kl(2gA2) is usually denoted as k* in the above equation. The values of k* for PRVs are provided as k,, (e.g., k* = 76.59kS) by the American Water Works Association approved PRV manufacturers. The operating modes and associated flow characteristics through a PRV can be described in terms of [I] as follows: Mode 1: fully closed PRV Q = 0 hPRV= 03 Mode 2: partially open PRV Q > 0 hPRV> k*Q2 Mode 3: fully open PRV Q > 0 hpRv = k*Q2 From the above flow-rate mode characterization in a PRV, it is apparent that there is a maximum flow rate for a given head loss across a fully open PRV. Alternately, the flow rate is less than the maximum flow rate for any other operating mode. Hazen - Williams friction factor The characteristics of pipe flow in network-analysis models are commonly described using the Hazen -Williams friction factor equation. Converting this equation to units compatible with the WATER model, one obtains

where bpi,, L, D , C, and Q are, respectively, the head loss in meters, the pipe length in meters, the pipe diameter in centimeters, the Hazen -Williams pipe friction factor, and the pipe flow rate in litre per second. For any pipe in a water distribution network, the values of L, D , and C remain constant and also remains hence the value of the term 160440L/(D4.865C1.85) constant. The use of [2] in the WATER model provides satisfactory estimates of head loss in pipes, but results in unacceptable flow

L 0w

-F Node- 1 (Elev.=200 m)

Node-2 (Elev.=100 m)

. I

" 7

0 Pipe-l (L=100 m, D=60 cm) U

Node-3 11

Pipe-2 (L=100 m, D=60 cm) Elev=100 rn

E

hi

Pipe-3 containing a PRV

N 0 D Node-5 (Elev.=190 m)

-

S Pipe-4 (L=100 m, D=30 c m )

F

N 0 Node-4

(Elev.=100 rn)

Node-6 D

Pipe-5 (L=100 m, D=60 cm) Elev.=100 m S

L 0 v-\

FIG. 1. Schematic of the test network.

rates in pipes containing PRVs. This problem in the WATER model and other similar network-analysis models emanates from their inability to account for the information on physical characteristics of PRVs. However, these models, including the WATER model, attempt to maintain the downstream pressure set point when the presence of a PRV is indicated in the pipe. This difficulty in the WATER model is illustrated below by using a test network. A test network To evaluate the performance of the WATER model in representing PRVs, a test network was created in the form of a computer model as shown in Fig. 1. The specifications of various pipes and PRVs used in the test network are listed in Table 1. Nodes 1 and 5 act as source nodes for representing a highpressure line and a low-pressure line respectively. Node 5 also serves the purpose of completing the network system loop, which is necessary for the WATER model to balance the head losses. Pipe 3 contains a PRV to be evaluated. Node 6 was used as demand node. By increasing the demand at node 6, the hydraulic grade line (HGL) at node 4 can be lowered to cause water flow through the PRV. The demand node 3 allows the lowering of the upstream HGL, whenever necessary. To ensure the flow of water through the PRV when the demand rate at node 6 exceeds the supply rate at node 5, the diameter of pipe 4 has been kept smaller than other pipes. Various tests were conducted on each of the three PRVs (Table 1) under bothlow (f 3 m) and high (f 10 m) differential head conditions. It is noted that the three PRVs have different diameters. The input data for these tests included the length, the diameter, the value of k for each pipe, and the downstream set point of 189 m. For low-head conditions, the elevation of the source node 1 was lowered to 192 m. Once the presence of a PRV is indicated in a pipe, the WATER model attempts to maintain the downstream set point. In regard to this attempt, the WATER model was found, as shown below, to allow a flow rate in far excess -= of the maximum allowable flow rate of an actual PRV. The test results along with corresponding portion of the maximum flow envelope are presented in Fig. 2. It is apparent from this figure that within a certain range of head loss in all the three PRVs, the WATER model allows an excessive flow rate compared with the maximum allowable flow rate for each one of the actual PRV. As stated earlier, this anomaly in flow rates in the WATER model is presently corrected based on a trial-and-error procedure. That is, the downstream set point of the pipe containing a PRV is successively lowered until the flow rate through the PRV is either less than or equal to the

TABLE1. Typical values of k and k* used in the test network


Pipes

L (m)

D (cm)

C

10 3 5

40.64 15.41 30.48

140 140 140

..

PRVs

k

kus

2.550 x 8.579 x 5.179 x

2.14 X 9.85 X 7.78 x

200

1.64 7.54 5.96

High

k*

Valve type

X X X

Ross PRV (40.64 cm) Clayton PRV (15.41 cm) Singer PRV (30.48 cm)

angel

Headloss Irn)

Headloss Irn)

Headloss I m )

Headloss ( m )

Headloss (rn)

Headloss ( m )

FIG.2. Comparison of flow rates through various types of PRVs using C values: ( a ) Clayton PRV; (b) Singer PRV; (c) Ross PRV. (-0-) flow rate through PRV; (-x-) maximum flow rate through PRV.

maximum allowable flow rate for the corresponding head loss across the PRV. The trial-and-error procedure in a large network system involving several PRVs requires numerous trials and thus renders the procedure tedious and time consuming. In the following, a procedure is presented wherein a composite value of the friction factor is sunnested for -pipes -containing PRVs.

Modified friction factors for pipes containing PRVs Case 1: Pipe containing a PRV Based on [ 2 ] ,the toal head loss, hl (= hpipe+ hPRV),in a pipe containing a PRV can be expressed as follows:

[3]

hl = [160440L/(D4.865C1.85)]Q1.85 + 76.45ku,Q2

-

Since the WATER model does n 8 accept the physical characteristics of a PRV, it is necessary to combine the available information on a PRV by modifying the Hazen-Williams friction factor as follows. [4]

hl = [ 1 6 0 4 4 0 ~ / ( D ~ . ~ ~ ~ C ; ~ ~ ~ ) ] Q l . ~ ~

In the above equation, the value of Ceq (i.e., equivalent C, which is the modified friction factor representing both the pipe an the PRV) is obtained from [3] and [4] as follows: [5]

Ceq= [1/C1.85+ 76.56~,D4.865Q0.15/(160440L)]-111.85

CAN. J. CIV. ENG. VOL. 17, 1990


550

H e a d l o s s fm)

H e a d l o s s fm)

H e a d l o s s fm)

Headloss

fm)

Headloss fm)

Headloss

fm)

FIG.3. Comparison of flow rate through various types of PRVs using C,, values: (a) Clayton PRV; (b) Singer PRV; (c) Ross PRV. flow rate through PRV; (-x-) maximum flow rate through PRV.

The only variable term in [4] and [5] is the flow rate, Q; thus the terms hl and Ceq become a function of the flow rate, Q, alone. However, one can develop a graphical relationship between Ceqand Q. From such a relationship one can choose the value of Ceq corresponding to the maximum allowable flow rate suggested by the PRV manufacturers. Selection of an appropriate value of the Ce ensures that the propagation error caused by the term Qo-lrin [5] is smallest in the vicinity of the maximum allowable flow rate. Since hl is a function of the flow rate Q, the error associated with its estimation is expected to be small when the flow rate drops within a narrow range of the maximum allowable flow rate. It is therefore reasonable to assume that an appropriate value of Ceqfor any pipe containing a PRV can be obtained by using [5]. From the above discussion, it is apparent that as the flow rate through a pipe containing a PRV approaches zero, the value of Ceq converges to the Hazen-Williams friction factor, C. Further, it is noted that one can develop an alternate equation for the modified friction factor based on Manning equation as discussed later.

Case 2. Pipes containing two PRVs in a parallel setting An installation of PRVs in parallel setting involves two

(-up)

PRVs connecting the high- and low-pressure lines. In this case, the downstream pressure set points in each of the two PRVs are designed such that one PRV (also called the "lead PRV") begins to operate first and subsequently reaches its full-wide-open condition before the second PRV (also called the "lag PRV") begins to operate. A setup consisting of a lead PRV and a lag PRV ensures that the PRVs are not alternately opening and closing, i.e., "hunting," when each PRV attempts to maintain the desired downstream set point. Based on the downstream set points, the time period during which both PRVs are operating can precisely be determined. When it is known that both PRVs are operating, the computational time of any network-analysis model and particularly the WATER model can be reducedby replacing the pipes containing PRVs by an equivalent single pipe. The head loss in a pipe containing either the lead PRV or the lag PRV follows [4] as expressed below:

where i = 1 and 2 respectively represent a pipe containing a lead PRV and a pipe containing a lag PRV. Since Q = Ql Q2, one obtains

+

TABLE2. Test results using modified friction factor for various types of PRVs High-range head loss


Head loss (m)

Recorded* flow (L/s)

Low-range head loss

Computedi flow (I-1~1

Error (%)

Head loss (m)

Recorded* flow (I-1~1

Computed+ flow (Lls)

Error (%)

Ross PRV (40.64 cm) 796.38 794.93 792.37 789.07 784.29 669.84 772.37 766.73 793.83 833.01 874.44 919.06 964.64

2.88 1.95 1.88 2.17 2.89 3.71 4.66 5.69

64.58 165.91 267.45 335.73 391.56 448.46 506.77 565.10

+1.5 1.9 +2.3 +2.7

+

Clayton PRV (15.41 cm) 117.52 117.26 116.61 115.58 114.26 118.60 128.30 138.92 161.73

2.00 1.95 2.20 3.44 4.99

3.02 28.04 48.98 62.40 76.25

-0.52 +O.M +0.66 +1.85

Singer PRV (30.48 cm) 421.54 416.30 407.03 393.42 397.76 421.16 474.18 530.68 588.41

-1.33 -0.43 +0.41 +1.25

2.00 1.96 1.85 1.70 2.42 3.27 4.26 5.39

3.26 53.32 103.55 152.26 184.00 216.62 249.83 283.48

*Recorded flow means flow value recorded in the field. 'Computed flow means flow value computed using the WATER model.

one can develop an alternate equation for the modified friction factor based on Manning equation as discussed later. Likewise, the flow rate, Q , through an equivalent pipe of diameter Dp and length Lp, and representing the combined effect of the pipes containing the lead PRV and the lag PRV, can be expressed as follows:

Since H, = Hi,, = Hi=2, one obtains the term Cpeqby combining [7] and [8] as follows:

The value of CPeqdepends on the choice of Lp and Dp. Intuitively, one can obtain these values by simple averaging as Lp = (L, + L2)/2 and D, = (D: + D : ) ~ .As noted earlier,

Case 3. Pipe containing any other water appurtenance The equation developed earlier for the term Cq in the case of a pipe containing a PRV can be extended to any water appurtenance or pipe restriction causing the head loss as follows:

where hpipe,L, D, C , Q , and k* are respectively the head loss in meters, the pipe length in meters, the pipe diameter in centimeters, the Hazen-Williams pipe friction factor, the maximum allowable pipe flow rate in litres per second and the head-loss coefficient for the water appurtenance. The term k* has units of m . s2/L2. For obtaining a reliable value of Ceq, as suggested earlier, one should develop a graphical relationship between Ceq and Q.

CAN. J. CIV.

552

ENG. VOL.

17, 1990


Modijiedfriction factors based on Manning equation for pipes containing PRVs Alternate equations for modified friction factors may be developed by expressing the head-loss equation of pipe flow in terms of the Manning equation as follows. where n is the flow-resistance coefficient commonly known as Manning's n, R is the hydraulic radius (equal to Dl4 in a fullflowing pipe), and other terms are the same as defined earlier. By employing [ I l l instead of [2], the alternate modifiedfriction-factor equations for the above-mentioned three cases are developed as follows.

Case 1. Pipe containing a PRV I

[12] neq= [n2

+(76.45k,,~~~~/~)/~]'

where neq (i.e., equivalent n ) is the modified friction factor representing both the pipe and the PRV, and the remaining terms are the same as defined earlier.

Case 2. Pipes containing two PRVs in a parallel setting

where npeq(i.e., parallel equivalent n ) is the modified friction factor representing two sets of pipes and PRVs in a parallel setting, and the remaining terms are the same as defined earlier.

Case 3. Pipe containing any other water appurtenance

The modified-friction-factor equations are independent of flow rate, Q, and therefore may be numerically evaluated for a specified geometry of pipes and PRVs. The need for a relationship between flow rate and modified friction factor is thus eliminated. This feature of these equations is attractive compared with earlier equations (i.e., [5], [9], and [lo]). However, it is noted that the limitations on the use of the Manning equation in water distribution networks are well recognized and such limitationss were recently elaborated by Higson (1983). Further, based on the theory of roughness, Higson (1983) suggests that the Manning equation should not be used in water distribution networks comprised of smooth pipe materials.

Evaluation of the effectiveness of the modified friction factors Case 1. Pipe containing a PRV The effectiveness of the modified friction factor, Ceq, in representing PRVs (Table 1) was tested in the WATER model by using the test network (Fig. 1). Tests were conducted for a variety of flow rates under both high and low differential headloss conditions. The flow rate through a PRV is obviously below its maximum allowable flow rate, when it is operating as a pressure-reducing device. However, the flow rate for a given head loss exhibits a relationships described by [3] for the case of a pipe containing a PRV with full-wide-open condition. The existence of the two-stage flow condition in a PRV is readily apparent in Fig. 3. In this figure the presence of a nearly vertical relationship between the flow rate and the head loss indicates the presence of pipe flow condition. Further, it is apparent from this figure that such a flow condition occurs

HEAD LOSS (m)

FIG.4. Comparison of flow rates through various types of PRVs in a parallel setting using Cpq values. (-+-) lead PRV; (-D-) lag lead PRV and lag PRV; (-A-) parallel PRVs. PRV; (-x-)

in a PRV prior to and up to its full-wide-open condition. At the full-wide-open condition and thereafter, the relationship deviates sharply to the right and from there on follows the curve described by the maximum allowable flow rate through a PRV. The error between the "theoretical" values of flow rate using [4] and the values of flow rate obtained using Ceqinstead of C in the WATER model was found to vary respectively from + 3 % to -0.4% and from - 1.2% to -7% (Table 2) for tests conducted under the high- and low-pressure differential ranges. The 7 % error appears to be unacceptably high; however, it occurs during the low-pressure differential range of a PRV and thus is inconsequential in network analysis. Based on the results of various tests, it is apparent that the use of the friction factor Ceq instead of C for a pipe containing a PRV in the WATER model provides a sound basis for network analysis and simulation.

Case 2. Pipes containing two PRVs in a parallel setting The adequacy of the use* Cpeqin representing PRVs in a parallel setting was tested in the WATER model by using the test network (Fig. 1). In this case, a 3 m long pipe contained the lead PRV (a Clayton PRV of 15.41 cm diameter) and another 3 m long pipe laid parallel to the previous pipe contained the lag PRV (a Singer PRV of 30.48 cm diameter). Tests on PRVs in a parallel setting were conducted by setting the downstream set point for the lead PRV at 187 m in the test network. For example, a typical test was conducted, first on the lead PRV with parameters similar to those described for the case of a pipe containing a single PRV until the set point of 187 m was realized. The attainment of this set point also


signaled the initiation of the lag PRV. In other words, this condition indicated a state when both PRVs were operating. Thus, whenever this condition was achieved, the values of parameters corresponding to the parallel PRVs were used to represent the operation of two PRVs in a parallel setting in the WATER program. Subsequently, the demand rate on the test network was increased to simulate its upper limiting value, i.e., a condition in which the test network was unable to maintain the set point of 187 m. Similar tests were conducted on each of the three PRVs and combinations of these PRVs. The following steps are helpful in illustrating the effectiveness of Cpeqin representing PRVs in a parallel setting in the WATER model. 1. Lead PRV opens and attempts to maintain the set point. 2. Lead PRV reaches its full-wide-open condition to maintain the set point. 3. Lag PRV reaches its initiation point. 4. Lag PRV opens and attempts to maintain the set point. 5. Lag PRV reaches its full-wide-open condition to maintain the set point. The above steps (1 -5) are exhibited by their corresponding numerals in Fig. 4. This figure contains a graphical relationship between the flow rate and the head loss for the lead PRV, the lag PRV, and the combined case of a lead PRV and a lag PRV. The values of flow rates exhibited in Fig. 4 were computed as follows. For the case when both PRVs were operating, the total flow rate was obtained using the value of Cpeqin [8]. The flow rate through the lead PRV was obtained by using an appropriate value of Ccq. Consequently, the flow rate through the lag PRV was obtained as the difference between the total flow and the calculated flow rate of the lead PRV. In Fig. 4, the close correspondence between various envelopes of allowable flow rates and the flow rate obtained using the WATER model for the parallel setting of PRVs is readily apparent. In other words, the closeness of comparison is indicative of the effectiveness of the suggested procedure for representing a set of PRVs in a parallel setting in the WATER model.

Application to the Greater Victoria Water District The Greater Victoria Water District (GVWD) is a water utility located in Victoria, B.C. It consists of high- and lowpressure systems. The high-pressure system is connected to the low-pressure system at three points: the Eslers storage, the Adams storage, and the Camden PRV station. A detailed description of the water distribution network; the specifications of various pipes, PRVs, storages, pumps, and other appurtenances; and the data used for calibration and validation is provided in the Appendix. The inflow rate in the water distribution is estimated to be 4671 Lls. Calibration tests based on pressures and flow rates recorded at 8:00 p.m. on August 7, 1987, (Table 3) were conducted with or without the use of Ceqand Cpeqvalues for representing PRVs in the GVWD network system (Appendix A). The GVWD system was assumed to be calibrated when the values of pressure and flow rate obtained using the WATER model and field recorded values at specified locations (Table 4) were within the limits suggested by Glaser et al. (1984). On the average, 10 trial runs were required (Appendix) to calibrate a simplified GVWD network system with the use of Ceq and Cpq. However, without the use of Ccqand Cpeq,50 trial runs were required (Appendix A) to calibrate the GVWD network system to specifications as noted earlier. In other words, the

use of Ccq and Cpeqreduced the number of trial runs by 5 times for the calibration of a simplified GVWD network system. The use of Ceqand Cpeqalso eliGinated the need for continuous adjustment of the downstream set points of the PRVs, when they had reached their full-wide-open condition.

Conclusions The use of modified friction factors, Ccqand Cpcq,provides an adequate basis for representing pipes containing PRVs in network-analysis models. A significant reduction in computational effort is achieved with the use of modified friction factors. Further, it is noted that the proposed modifications do not require any alteration to the model structure. The values of modified friction factors for any specified network representation containing an appurtenance are provided to the model through the input data files. Acknowledgements The author is thankful to the GVWD authority for allowing the use of the WATER model and data sets in various calibration and validation runs and to B. Keenan for his excellent computational efforts in various phases of this project. The partial financial support for the project provided by the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged. BOND,R. G., and STRAUB, C. P. 1973. Handbook of environmental control. Vol. 111. Water supply and treatment. CRC Press, Cleveland, OH. BOYLE,W. P. 1986. Applied fluid mechanics. McGraw-Hill Ltd., Toronto, Ont. CROSS,H. 1936. Analysis of flow in networks of conduits or conductors. Bulletin #286, Experimental Station, University of Illinois, Urbana, IL. EPP, R., and FOWLER, A. G. 1970. Efficient code for steady-state flows in networks. ASCE Journal of the Hydraulics Division, 96(HYl): 43-56. P. A., VASCONCELOS, J. J., MONTGOMERY, GLASER, H. T., NAECKER, J. M., and GILLETTE, S. J. 1984. The role of calibration in water distribution systems analysis. American Water Works Association, Denver, CO. GUPTA, S., MCBEAN, E. A., and COUSINS, J. R. 1980. Mathematical efficiency concerns inwater distribution network considerations. Canadian Journal of Civil Engineering, 7: 78 - 83. HIGSON, K. 1983. The theory of roughness: historical background and recent innovations. Department of Engineering, University of Lancaster, Lancaster, United Kingdom. A N D ASSOCIATES. 1981. Triangle mountain water KER,PRIESTMAN distribution study. Consulting Engineers, Victoria, B.C. MUNICIPAL HYDRAULICS. 1982. WATER, users manual. Municipal Hydraulics, Vancouver, B.C. SIMON,A. L. 1981. Practical hydraulics. John Wiley & Sons Inc., Toronto, Ont. T.T=1979. Water supply and sewerage. STEEL,E. W., and MCGHEE, 5th ed. McGraw-Hill Book Co., New York, NY. WILLIS,CUNLIFFE, TAITA N D ASSOCIATES. 1980. Triangle mountain water study. Consulting Engineers, Victoria, B.C.

Appendix. Evaluation of the effectiveness of the modified friction factors in the case of the Greater Victoria Water District network system The Greater Victoria Water District (GVWD) is a water utility located on the outskirts of Victoria, B.C. It serves three main functions: (1) management and maintenance of the reservoirs existing in the watersheds of Sooke Lake and the Gold-

CAN. 1. CIV. ENG.


554

VOL. 17,

1990

AREA SERVED BY GREATER VlCTORlA WATER DISTRICT UNDER WATER TARIFF EXEMPTIONS FROM GREATER VICTORIA WATER DISTRICT

FIG.

Al. Area served by the Greater Victoria Water District.

stream Lakes; (2) management and maintenance of the primary water distribution or trunk mains carrying water from the above watersheds into the City of Victoria, Municipality of Saanich, Township of Esquimalt, Municipality of Oak Bay, and the provincial Capital regional district (Fig. Al); (3) operation and maintenance of the secondary distribution system that supplies water to homes and businesses in the electoral areas of Colwood, Metchosin, Langford, and View Royal (Fig. Al). A brief description of the GVWD physical system The GVWD water distribution network system consists of high- and low-pressure systems. The primary (main) pipeline for the high-pressure system (main No. 4) is a 122 cm (48 in.) diameter steel pipe, which originates at the Japan Gulch reservoir and extends along Goldstream Avenue and Atkins Avenue and then runs parallel to the Trans-Canada Highway before heading north to the Saanich Peninsula. A balancing tank, Haliburton Reservoir, is connected to main No. 4 near the Cherry Tree Bend meters (Fig. A2). The low-pressure system consists of two primary mains: (1) main No. 3 is a 99 cm (39 in.) diameter steel pipe and (2) main No. 1 is a 91 cm (36 in.) diameter steel pipe which is lined with cement mortar for the majority of its length. Both mains originate at Humpback Reservoir and run parallel to each other along Station Avenue and Goldstream Avenue (Fig. A2). Main No. 1 turns near Wale Road to follow Atkins Avenue and then runs parallel to main No. 4 to Burnside. At this location, main No. 1 heads east through the Adams venturi meter and then follows Burnside Road to the Cecelia meter. Main No. 3 extends along Wale Road, the Island Highway, and then the Trans-Canada Highway where it passes through the St. Giles meter. From here main No. 3 travels

beside main No. 1 and along Burnside Road, Hampton Road, Boleskine Road, Tennyson Avenue, Dupplin Road, Douglas Street, Tolmie Avenue, Cook Street, Finlayson Street, North Dairy Road, Frechette Street, and Lansdowne Road where it feeds the Oak Bay flow meters. Main No. 3 terminates at the Mount Tolmie Reservoir (Fig. A2). Between the Japan Gulch and Humpback reservoirs and line meters at Burnside (main No. 4), St. Giles (main No. 3), and Adams storage (main No. l), the side outlets feed the secondary distribution system that serves View Royal, Colwood, Langford, and Metchosin (Fig. A2). The higher pressure system is connected to the low-pressure system at three points, the Eslers PRV station, The Adams storage PRV station, and the Camden PRV station. The PRVs are preset to enable the high-pressure system to feed water flow into the low-pressure system to maintain a desired minimum pressure in the low-pressure system when necessary. The location of all three PRV stations is shown in Fig. A2.

Physical data on the GVWD system for network modeling The information on various elements of the GVWD water network was obtained as follpws. The pertinent physical data on the primary water distritfbtion mains were obtained from construction profiles and contract drawings maintained by the GVWD head office. The data on the remainder of the system were obtained from 1:2500 scale topographic base maps containing the general pipe information on the GVWD system. However, where precision data were required such as the centerline elevation of pressure meters, field surveys were conducted. The physical data set, in SI units, was assembled for use in the numerical simulation of the GVWD network system. For example, SI units for various elements were used as follows: the pipe length, the nodal elevation, and the hydraulic grade


Movnl T o h a

o*

BJ"

NODESAREACNIV REFERENCE WlNTS FOR N4MES OF PRESSURE METERS AND n o w M m n s

FIG.A2. Basic water distribution network of GVWD for analysis.

line elevation in meters, the inside pipe diameter in centimeters, the pipe flow rate in litres per second, the velocity in meters per second, and the pressure in kiloPascal. The physical data set for use in the WATER model was grouped into two parts: pipe and nodes. A pipe with fixed length and diameter and uniform friction factor was considered to be a section of pipeline with a node at each end. Inside pipe diameters have been used in all pipes in the model. The diameter of main No. 1 was reduced-by 2.5 cm (1 in.) to allow for the cement mortar lining. The Hazen-Williams friction factors for various pipes used in the network simulation are those given by Simon (198 1). Nodal considerations and elevations with the secondary systems and for the major intakes were obtained based on methods of data abstraction described elsewhere (Keenan1) for assembling the required data set on the GVWD svstem. Water demands at nodal points were obtained by considering two types of demands, metered and unmetered. Water demands at various locations were obtained from flow data recording

'Keenan, B. F. 1988. Water distribution network modeling. An unpublished report, Department of Civil Engineering, Lakehead University, Thunder Bay, Ont.

charts. However, unmetered demands in residential areas were estimated based on water consumption rate suggested by Bond and Straub (1973), whereas such demands in industrial areas were estimated based on the recommendation of Steel and McGhee (1979). However, some correction factors were used based on the suggestions (Willis, Cunliffe, Tait and Associates 1981; Ker, Priestman and Associates 1982) for residential areas in Victoria.

Characteristics of PRVs in the GVWD system As described earlier, there are three main pressure-reducing stations in the GVWD network system. Each of the PRV stations at Eslers and Camden has two PRVs in a parallel setting, and the Adams storageTRV station has a single PRV. The values of Ceqand Cpeqused at the three PRV stations are as follows. Eslers PRV Station Lead PRV (15.41 cm Clayton PRV with a set point of 105.032 m and connected with a 3 m long pipe of diameter 15.41 cm): Ceq = 28.50. Lag PRV (30.48 cm Singer PRV with a set point of 103.625 m and connected with a 3 m long pipe of diameter 30.48 cm): Ceq = 17.073. Parallel PRVs setting with a set point of 103.625 m and

556

CAN. J. CIV. ENG.

TABLEA l . Summary of flow meter and pressure meter recordings for 8 p.m. on August 7, 1987

TABLEA2. Comparison of model results and field data recordings Flow ( ~ 7 s )


Flow or pressure meter (A) Flow meter recordings Japan Gulch Humpback No. 3 Humpback No. 1 St. Giles Adams Storage Brunside

Recorded flow (Lls) or pressure (psi)" 2216 1434 1022 1173 892 1053

Node number 1 200 250 228 273 32

(B) Pressure meter recordings Adams Storage Admirals Beaver Lake Bmnside Cairndale Pump Camden PRV (Downstream) Cecelia Cook Street Dooley Eslers PRV (Downstream) Fulton Pump Glen Forest Way Haliburton Langford Fire Hall Langford Fire Hall No. 2 Lay ritz Lombard Markham Mill Hill Mount Tolmie Oak Bay Pears Pump Rason Pump Rocky Point Shaw Road St. Giles View Royal Fire Hall Walford Wishart *I psi

=

6.89 kPa.

connected with a 3 m long pipe of diameter 34.154 cm: C,,, = 16.184.

Adams Storage PRV Station Single PRV (30.48 cm Singer PRV with a set point of 103.543 m and connected with a 5 m long pipe of diameter 30.48 cm): Ceq = 22.34. Camden PRV Station Lead PRV (30.48 cm Clayton PRV with a set point of 101.19 m and connected with a 10 m long pipe of diameter 30.48 cm): Ceq = 31.98. Lag PRV (40.54 cm Ross PRV with a set point of 98.38 m and connected with a 10 m long pipe of diameter 40.64 cm): CCq= 17.073. Parallel PRVs setting with a set point of 198.38 m and connected with a 10 m long pipe of diameter 50.80 cm: Cpeq= 24.79.

Flow or pressure meter Japan Gulch Humpback No. 3 Humpback No. 1 St. Giles Adams Storage

Field recorded

Model computed

(a) Flow data 2216 243 1 1434 1333 1022 906 1173 1182 892 882

Error (%)

Pressure difference (psi)*

+9.7 -7.0 -11.3 +0.8 -1.1

(b) Pressure data

Eslers PRV (No. 4) Camden PRV (No. 4) Brunside Layritz Markham Beaver Lake Haliburton Dooley Adams Storage PRV (No. 3) St. Giles Oak Bay Mount Tolmie Cook Street Camden PRV (No. 1) Cecelia Eslers PRV (No. 3) Adams Storage PRV (No. 4) Admirals

-3.2 -2.5 -7.2 -5.2 - 15.2 -3.0 -6.2 -4.5

*I psi = 6.89 kPa.

Variables and calibration limits used in the GVWD system Flow rate and pressure are used as the calibration variables in the GVWD network system. An event recorded at 8:00 p.m. on August 7, 1987, was used for model calibration. The selection of this event for calibration was based on two considerations. First, the reliability of flow recordings for this event was deemed high because all the flow meters in the primary distribution network were checked and calibrated during June and July of 1987; second, this event was considered ideal for calibration because unusually high flows were recorded at the intake flow meters. A summary of flow and pressure recordings at specified locations in the GVWD system is provided in Table A1 . The calibration limits as means of assessment of the agreement between the model results and field recordings were those suggested by Glaser et al. (1984). These limits are as follows: For the accuracy of pressure calibration, the mean absolute pressure variance less than 34.5 kPa (5 psi) and maximum pressure variance of less than 69 kPa (10 psi) is specified to be desirable. On the other hand, for the accuracy of flow calibration, the flows at specified locations in primary pipelines should be within 10% for high-flow condition. GVWD network calibration wtih the use of modified friction factors A computer representation of the GVWD network was developed using physical data on various elements of the network as described earlier. In summary, there were a total of 532 pipes and 523 nodal points defining the GVWD network


PANU

system (Fig. A2). The flow rate in the water distribution network was estimated to be 4671 Lls for the event used for calibration. Specifically, the main concern in this paper, the PRVs, were represented as follows. The Eslers PRVs were set up in a parallel setting using the modified Hazen-Williams friction factor, Cw = 16.184, pipe diameter, D = 34.154 cm, pipe length, L = 3 m, and a PRV set point of 103.625 m. At Adams Storage PRV station a single PRV was set up using C,, = 22.34, D = 30.48 cm, L = 5 m, and a PRV set point of 103.543 m. The Camden PRVs were set up in a parallel setting using C,,, = 24.79, D = 50.80 cm, L = 10 m, and a PRV set point of 98.38 m. The use of modified friction factors eliminated the need for a constant check to ensure that a legitimate flow rate was occurring through a numerical PRV. However, to obtain specified flow rates and pressures at various locations in the network, the values of the Hazen-Williams friction factor, C, for various pipes forming the network were adjusted in the model to represent the roughness characteristics of these pipes in the GVWD system in the field. On the average, ten trial runs were required to calibrate a simplified GVWD network system (Fig. A2) with the use of C,, and C,,,. Table A2 provides a summary of the errors for flows and pressures between the network model results (obtained at the end of tenth trial run) and the flow and pressure recordings made at 8:00 p.m. on August 7 , 1987, at vari-

557

ous locations in the GVWD network system. The results of the tenth trial run in Table A2, on a comparative basis, can be considered staisfactory for pressures. Kowever, it is noted that substantial errors in pressure exist at the Markham and Oak Bay pressure meters. Field investigations indicated that both of these meters are of similar old vintage and thus it is suspected that the field recordings at these meters are in error. It is apparent from Table A2 that flows at the intakes, on the average, are in error by 9.7%. While such a magnitude of error is far from ideal, it does represent the result of an attempt to maintain the same pressure in the main #4 as was recorded in the field.

GVWD network calibration without the use of mod$ed friction factors In this case only the Hazen-Williams friction factor, C, was used to represent the roughness characteristics in all pipes, irrespective of whether containing a PRV or not. As noted earlier, there is a constant need to check on the legitimacy of flow rate through a PRV. In addition, on the average, 50 trial runs were required (Keenan') to achieve the same level of calibration as summarized in Table A2 for the case of the modified friction factors, where only 10 trial runs were needed. A five-time reduction in computational effort suggests the effectiveness of the procedure suggested in this paper.